Abstract: To enhance the detection capability for weak underwater targets, sonar system design is shifting from a "hardware-centric" approach toward high-sensitivity algorithms such as matched-field processing. This transition, however, reveals a profound dilemma: in dynamically uncertain ocean environments, the pursuit of high sensitivity leads to a "performance cliff" caused by environmental mismatch, while the pursuit of high robustness inevitably suppresses faint target signals. This fundamental trade-off is formally defined as "The Second Sonar Paradox: the Sensitivity–Robustness Conflict." By establishing a theoretical framework that distinguishes between uncertainty and unmeasurability, this paper identifies the root cause of the paradox as "unknown unknowns," and develops a mathematical model to derive a core performance bound constrained by unmeasurability. The study demonstrates the inherent unsolvability of this paradox within conventional paradigms from three perspectives: the intrinsic properties of the environment and target, the rigidity of traditional system design, and the ill-posed nature of the underlying mathematical problems. To overcome this impasse, we propose a collaborative resolution strategy built upon two pillars: joint target en dash environment estimation and entropy-driven regularization. Building on this, we formulate the "Cognitive Collaboration" paradigm and its closed-loop operational mechanism, providing a comprehensive theoretical and systemic framework for unifying high sensitivity and high robustness in dynamic environments. This work marks a paradigm shift in sonar technology—from "static confrontation" to "dynamic cognition."